This is the classic science fair project that just never seems to be allowed by the teacher running the fair.

Perhaps the reason that it never flies is because it defies the scientific method. Making an observation is qualitative, rather than quantitative. The question is the cat burning or not rather than how much is the cat burning? How does one measure the burning to determine if they are making progress? Some cats are louder than others. Can one make a hypothesis? Not really. The cat is very like Schrodinger's Cat. It is either going to burn, or not burn. You can't tell until you light it on fire. But doing so destroys the cat, making another test impossible. Hence one cannot reproduce the results. How does one know that the fireproofing method fails on all cats?

Perhaps the reason it is never allowed is because the teacher doesn't want to deal with the ASPCA.

I think the real reason is that people are afraid of progress. What would happen if cats could be flame proofed? What if there were some kind of nomex cat sweater? Someone would make a fortune until some owner didn't dress the cat correctly and that would be the end of the cat. Then the lawsuits would follow, and then no one would ever want to be on the cutting edge of science and technology again.